2

We adopt the convention that the first coordinate $i$ increases as one goes downwards, and the second coordinate $j$ increases as one goes from left to right.

The index increases by 1 when the path is crossed from right to left.

The numbers inserted in $L$ must increase strictly down each column.

Also, $F$ does not increase distances.

There has recently been increasing interest in the theory of ......

It becomes impracticable to compute the zeros of $F$ for degrees greater than 6; in any event, deciding whether the divisors found in this way represent irreducible curves becomes increasingly difficult.

Indeed, as $n$ increases, it becomes increasingly rare for a manifold to be a hyperplane section of another projective manifold.